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A169677 The first of a pair of sequences A and B with property that all the differences |a_i - b_j| are distinct - for precise definition see Comments lines. 6
0, 1, 7, 18, 35, 59, 88, 125, 178, 233, 285, 344, 352, 442, 557, 675, 796, 797, 957, 1011, 1220, 1411, 1564, 1579, 1888, 2120, 2152, 2503, 2829, 2953, 3393, 3464, 3593, 3724, 4237, 4956, 5310, 5388, 5968, 6478, 6756, 7344, 7698, 8004, 8182 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Consider pairs of sequences A = a_1 a_2 a_3 a_4 ... and B = b_1 b_2 b_3 ... such that

1: All the terms are nonnegative integers

2: The terms of A are strictly increasing

3: The terms of B are strictly increasing

4: All the numbers |a_i - b_j| are distinct

5: The terms are computed in the following order: a(1), b(1), a(2), b(2), ..., b(n-1), a(n), b(n), a(n+1), ... and always the smallest value is chosen that satisfies constraints 1-4.

Computed by Alois P. Heinz and Wouter Meeussen, Mar 27 2010

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..200

MAPLE

# Maple program from Alois P. Heinz:

ab:=proc() false end: ab(0):=true:

a:= proc(n) option remember;

local ok, i, k, s;

if n=1 then 0

else b(n-1);

for k from a(n-1)+1 do

ok:=true;

for i from 1 to n-1 do

if ab(abs(k-b(i))) then ok:= false; break fi

od;

if ok then s:={};

for i from 1 to n-1 do

s:= s union {abs(k-b(i))};

od

fi;

if ok and nops(s)=n-1 then break fi

od;

for i from 1 to n-1 do

ab(abs(k-b(i))):=true

od;

k

fi

end;

b:= proc(n) option remember;

local ok, i, k, s;

if n=1 then 0

else a(n);

for k from b(n-1)+1 do

ok:=true;

for i from 1 to n do

if ab(abs(k-a(i))) then ok:= false; break fi

od;

if ok then s:={};

for i from 1 to n do

s:= s union {abs(k-a(i))};

od

fi;

if ok and nops(s)=n then break fi

od;

for i from 1 to n do

ab(abs(k-a(i))):=true

od;

k

fi

end;

seq(a(n), n=1..80);

seq(b(n), n=1..80);

MATHEMATICA

ClearAll[ab, a, b]; ab[_] = False; ab[0] = True; a[n_] := a[n] = Module[{ ok, i, k, s}, If[ n == 1 , 0, b[n-1]; For[ k = a[n-1] + 1 , True, k++, ok = True; For[ i = 1 , i <= n-1, i++, If[ ab[Abs[k - b[i]]] , ok = False; Break[] ]]; If[ ok , s = {}; For[ i=1 , i <= n-1 , i++, s = s ~Union~ {Abs[k - b[i]]}; ]]; If[ ok && (Length[s] == n-1) , Break[] ]]; For[ i=1 , i <= n-1 , i++, ab[Abs[k - b[i]]] = True]; k]]; b[n_] := b[n] = Module[{ ok, i, k, s}, If[ n == 1 , 0, a[n]; For[ k = b[n-1] + 1 , True, k++, ok = True; For[ i=1 , i <= n, i++, If[ ab[Abs[k - a[i]]] , ok = False; Break[] ]]; If[ ok , s = {}; For[ i=1 , i <= n , i++, s = s ~Union~ {Abs[k - a[i]]}; ]]; If[ ok && Length[s] == n , Break[] ]]; For[ i=1 , i <= n, i++, ab[Abs[k - a[i]]] := True]; k]]; Table[a[n], {n, 1, 45}] (* Jean-Fran├žois Alcover, Aug 13 2012, translated from Alois P. Heinz's Maple program *)

CROSSREFS

Cf. A169678, A169679, A169680, A169690-A169693.

Sequence in context: A225286 A000566 A225248 * A263876 A192751 A272459

Adjacent sequences:  A169674 A169675 A169676 * A169678 A169679 A169680

KEYWORD

nonn,nice

AUTHOR

R. K. Guy and N. J. A. Sloane, Mar 27 2010

EXTENSIONS

Comments clarified by Zak Seidov and Alois P. Heinz, Apr 13 2010.

STATUS

approved

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Last modified March 23 21:31 EDT 2017. Contains 283985 sequences.